Grigory Perelman is:

A Russian, born in 1966.

Careful, disciplined and precise in his thinking, ever since his childhood. Since a young age, he’s already quite uninterested in the “real” world, because the only world to him is Math.

Won IMO 1982’s gold medal - and he’s known for “there is no Math question he can’t solve”  (I guess, no high school Math question).

A geometry type of Mathematician: he solves problems using shapes, drawing lines, etc. This explains why he’s born for Topology, a field of Math that concerns a lot of shapes and dimensions. 

Was exceptionally lucky in his journey to the top: without the help and protections of his Math teachers in secondary, high school, university and post-doc period, as well as lucky situations (compared with other people in his generation), he couldn’t have had the chances necessary to develop himself into one of the world’s most superb geometricians. 

Solved the Soul Conjecture in 1994, at the age of 28. This made him the recipient of the European Math Society’s Award. But he rejected, stating that he was ‘not ready’. 

After that, he worked on what is called “Alexandrov space” but that didn’t make any headway.

For an extended period from 1994, Perelman quietly worked on the Poincaré Conjecture.

Poincaré Conjecture is one of the most important and difficult open problems in Topology, and geometry in general. Since Henri Poincaré raised this hypothesis in 1904, the answers have been confirmed for dimensions >= 4 thanks to the contributions of various mathematicians. The Conjecture, which was stated for dimension of 3, is still without the answer. This makes it included in the list of the 7 problems carrying the 1 million USD price tag for a correct answer challenged by Clay Math Institute. 

In Nov 2002 Perelman uploaded a series of paper proving the Poincaré Conjecture is correct. He actually proved a more general statement known as the “geometrization conjecture”, of which the Poincaré Conjecture is a corollary. His proof made extensive use of mathematician Hamilton’s work on what is called as “Ricci Flow”. He thus spent 8 - 9 years working on this problem, in absolute solitude. 

In 2006, his proof was verified by the top scholars in the field as correct. 

In June 2006, 2 mathematicians in China also published a paper claiming that they themselves have found the solution to the Geometrization and Poincaré Conjectures. They later published an erratum and retracted their original title. As it turned, they seemed to have followed quite closely an explanation of Perelman’s proof by Klein and Lott, but forgot to cite the source. 

International Math Union (IMU)’s 2006 congress awarded Perelman the Fields Prize, together with 3 other mathematicians (The Fields Prize is awarded to 2 - 4 Mathematicians every 4 years). Perelman, however, rejected the prize. 

In 2010, Clay Institute awarded him 1 million US$. However, he once again rejected. 

It’s now rumored that because some of the messy things after his proof published in 2002, Perelman has now severed contacts with everyone, except his mother. He’s also rumored to have said he’d abandon Math entirely.  In an interview with the New Yorker back in 2006, he was quoted to have said about the publications of the 2 authors who originally claimed their proof of the Poincaré Conjecture: ”I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest”. 

His story is fascinating and the aboves are just some note-worthy points in his long journey. You should hence check out this book  Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century by Masha Gessen.

It will also give you a glimpse into Russian Math society in the middle and late 20th century.